How to Integrate Arcsin Functions: Solving the Integral of Arcsin (2x/(1+x^2))

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Homework Help Overview

The discussion revolves around evaluating the integral of the arcsine function, specifically \(\int \arcsin \left(\frac{2x}{1+x^{2}}\right)\). The subject area is integral calculus, focusing on techniques for integrating complex functions.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • The original poster expresses uncertainty about how to start the integration process and mentions complications arising from substitution attempts. Some participants suggest using integration by parts, while others caution against directly substituting into the arcsine equation.

Discussion Status

The discussion is ongoing, with participants offering different approaches and raising questions about the validity of certain methods. There is no explicit consensus, but guidance on integration by parts has been introduced.

Contextual Notes

Participants are navigating the complexities of integrating a function involving arcsine, with some noting the potential messiness of the process. The original poster's uncertainty indicates that they may be facing challenges with the integration techniques involved.

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Homework Statement


Evaluate [tex]\int arcsin (\frac{2x}{1+x^{2}})[/tex]

Homework Equations


[tex]\int arcsin x = xarcsinx +\sqrt{1-x^{2}} + C[/tex]

The Attempt at a Solution


I'm not sure where to begin, when I try to substitute the term inside the brackets the equation gets even more complicated. Help?
 
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Are you familiar with integration by parts? The relevant equation you stated uses parts by using u = arcsin x and dV = dX.

Do the same procedure with your above integral... though you are correct that it does get messy!
 
You can't just substitute into the equation for arcsin x, it doesn't work that way
 
Thank you =)
 

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